How to UV unwrap this object and how to have the same textures resolution for the two objects
Ok so I'm guessing you mean relative UV scale between the two separate mesh objects when you say same resolution.
But first we need to clarify what you mean by &quot;share the same UV layout after&quot;.
Do you
A. mean that you want the UVs to overlap or sit on top of each other in the UV space like this.

Or B.
Have their own separate islands but on the same UV map like this

I got this result by using blender 2.8 new feature that allows going into edit mode of multiple meshes at once and a combination. of uv mapping operation.
So in edit mode of both mesh objects, first using project from view, from the back with just the faces along the center point of mesh since its a mirrored mesh. Then using constrain to proportions, move to one side, then move to center using snapping to align that center line of mesh with center of x axis like in screenshots. Making sure when you scale them to scale them together.
Next I take all those uvs in the uv editor and hit p to pin them in place (the red verts in UV editor), then select all faces, and run unwrap. This will keep the pinned UV verts in place and fill in the rest linked faces with usual unwrapping.
Then we can use the mirror modifier setting for flip U to automatically mirror the UV to the other side like this.

https://drive.google.com/file/d/1a5dIbtKAD47t3x--GEjsx9qR0oqUPT-V/view?usp=sharing